On testing the strong accessibility of a nonlinear control system

In this paper we show that a couple of matrices A, B (a `dynamic´ and a `control´ matrix), whose components are in general functions of both state and control variables, can be associated to any stationary nonlinear system whose system function is meromorphic (e.g. all components are ratios of analytic functions) in a way consistent with linear systems theory, and such that the test of accessibility (from a point p of the system domain) can be carried out formally as the controllability test for linear systems: the controllability matrix is build up and the full rank condition checked at the point p. This allows to make the test noticeably easier than the classical accessibility tests so far available in the literature. Further, it is proved that the accessibility from a point p implies the accessibility from every point of the largest open convex subset of the system domain including p, which, for the sub class of σπ-systems (in Rⁿ) can be readily determined as a certain union of orthants of Rⁿ.